What happened to me is that my customer's system had Vdd of 2.9V, and I had no problem to program it with Link2. However, after they changed the Vdd to 3.4V, I couldn't program with Link2. Do you know what might be the cause?

Aren't the important lines SWCLK and SWDIO buffered by a 74LVC2T45 between the LPC4370 and the connector? So, for the levels, shouldn't you be reading the 74LVC2T45 datasheet, not the LPC4370 datasheet?